Substrate resistance modeling for noise coupling analysis

Accurate substrate modeling is of utmost importance for substrate noise coupling analysis in mixed-signal circuits. In this paper we present a two-port Z-parameter model based on a physical description of the substrate surface potential. The Z-parameter model is expressed using a one-port semiempirical resistance model. This resistance model accurately describes the observed initial increase in resistance followed by the observed saturation as the contact separation increases. The Z-parameter model was compared to measurement data obtained from a set of CMOS test structures. The model fits measured results well, in contrary to when resistive networks are used to represent the substrate. Furthermore, we show that the substrate coupling between a digital circuit and an analog circuit does not have to become zero as the distance between the circuit blocks increases, instead the coupling between the circuits approaches a constant non-zero value.